Constrained multi-agent ergodic area surveying control based on finite element approximation of the potential field

Heat Equation Driven Area Coverage (HEDAC) is a state-of-the-art multi-agent ergodic motion control guided by a gradient of a potential field. A finite element method is hereby implemented to obtain a solution of Helmholtz partial differential equation, which models the potential field for surveying motion control. This allows us to survey arbitrarily shaped domains and to include obstacles in an elegant and robust manner intrinsic to HEDAC's fundamental idea. For a simple kinematic motion, the obstacles and boundary avoidance constraints are successfully handled by directing the agent motion with the gradient of the potential. However, including additional constraints, such as the minimal clearance dsitance from stationary and moving obstacles and the minimal path curvature radius, requires further alternations of the control algorithm. We introduce a relatively simple yet robust approach for handling these constraints by formulating a straightforward optimization problem based on collision-free escapes route maneuvers. This approach provides a guaranteed collision avoidance mechanism, while being computationally inexpensive as a result of the optimization problem partitioning. The proposed motion control is evaluated in three realistic surveying scenarios simulations, showing the effectiveness of the surveying and the robustness of the control algorithm. Furthermore, potential maneuvering difficulties due to improperly defined surveying scenarios are highlighted and we provide guidelines on how to overpass them. The results are promising and indiacate real-world applicability of proposed constrained multi-agent motion control for autonomous surveying and potentially other HEDAC utilizations.